MAUMEE, Ohio — President Obama declared victory Thursday in the two-year fight over his health care reform bill, declaring at a campaign rally that “the law I passed is here to stay.”

View Photo Gallery: In advance of Friday’s release of the June jobs report, the president commenced his two-day “Betting on America” tour of northern Ohio and western Pennsylvania, where he is defending his economic policies and health-care law.

Obama told a crowd of about 500 supporters in this town just south of Toledo that he was willing to work with critics to improve the legislation that requires all Americans to purchase health care.

But he vowed that there was no turning back on the law, despite heavy opposition from Republicans who have vowed to try to repeal it in Congress. The Supreme Court upheld the legislation’s core provision, the individual mandate, in a 5-4 ruling last week that gave the Obama administration a political and policy victory just months before the election.

The law “is going to make the vast majority of Americans more secure,” Obama said. “We will not go back to the days when insurance companies could discriminate against people just because they were sick.”

He added that “now is not the time to spend four more years refighting battles we fought two years ago.”

The GOP has continued to criticize the law, charging that it essentially imposes a tax on people by requiring them to purchase health-care coverage or face a fine. That stance has put Obama’s Republican challenger, Mitt Romney, in a tricky position because he authored a similar law during his tenure as governor of Massachusetts.

The White House, while celebrating the court’s ruling, refused to embrace the justices’s view that the individual mandate can be viewed as a tax, even though that judgment is the reason the law was not declared unconstitutional. The Court decided that the individual mandate should be allowed under the federal government’s ability to impose taxes.

On Thursday, President Obama’s campaign spokesman Ben LaBolt reiterated the White House’s position that the mandate is a penalty rather than a tax.

“You saw our arguments before the court,” LaBolt said during an appearance on CNN’s “Starting Point with Soledad O’Brien.” “At no point did any of the government lawyers say it was a tax.”

During oral arguments, U.S. Solicitor General Donald Verrilli walked a thin line between saying the penalty was a valid exercise of Congress’s taxing power that had the “characteristics” of a tax, and declining to answer directly whether it was a tax. At times, he seemingly tied himself in knots to differentiate between the two.

At one point during the arguments, Justice Antonin Scalia asked Verrilli directly, “Is it a tax or not a tax? The President didn’t think it was.”

Verrilli answered that “the President said it wasn’t a tax increase because it ought to be understood as an incentive to get people to have insurance. I don’t think it’s fair to infer from that anything about whether that is an exercise of the tax power or not.”